interface NtildeProof<T> {
    alpha: T[];
    t: T[];
}
interface NtildeProofs<T> {
    h1WrtH2: NtildeProof<T>;
    h2WrtH1: NtildeProof<T>;
}
interface Ntilde<T> {
    ntilde: T;
    h1: T;
    h2: T;
    ntildeProof?: NtildeProofs<T>;
}
export declare type DeserializedNtildeProof = NtildeProof<bigint>;
export declare type DeserializedNtildeProofs = NtildeProofs<bigint>;
export declare type DeserializedNtilde = Ntilde<bigint>;
export declare type DeserializedNtildeWithProofs = Omit<DeserializedNtilde, 'ntildeProof'> & {
    ntildeProof: DeserializedNtildeProofs;
};
export declare type SerializedNtildeProof = NtildeProof<string>;
export declare type SerializedNtildeProofs = NtildeProofs<string>;
export declare type SerializedNtilde = Ntilde<string>;
export declare type SerializedNtildeWithProofs = Omit<SerializedNtilde, 'ntildeProof'> & {
    ntildeProof: SerializedNtildeProofs;
};
export interface RSAModulus {
    n: bigint;
    q1: bigint;
    q2: bigint;
}
export interface RangeProof {
    z: bigint;
    u: bigint;
    w: bigint;
    s: bigint;
    s1: bigint;
    s2: bigint;
}
export interface RangeProofWithCheck {
    z: bigint;
    zprm: bigint;
    t: bigint;
    v: bigint;
    w: bigint;
    s: bigint;
    s1: bigint;
    s2: bigint;
    t1: bigint;
    t2: bigint;
    u: bigint;
}
export {};
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